Solve a 2nd order Ordinary Differential Equation

In summary, the conversation discusses a differential equation involving a function with its first and second derivatives, along with two constants C1 and C2. The conversation also mentions the use of the exponential function, denoted as "exp". The attempt at a solution involves substitution and simplification to find a solution for the equation.
  • #1
physicsguy43
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0

Homework Statement


Y''-((Y')^2)+(C1*exp(Y))=C2

C1 and C2 are constants.
exp = e

Homework Equations


No clue how to start this

The Attempt at a Solution


Y'=A=dY/dt
Y=At+C3 (not sure)

A'-(A^2)+C1exp(At+C3)-C2=0
A'-(A^2)+C1exp(C3)exp(At)=0
let C=C1*exp(C3)
A'-(A^2)+Cexp(At)=0
 
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  • #3
physicsguy43 said:

Homework Statement


Y''-((Y')^2)+(C1*exp(Y))=C2

C1 and C2 are constants.
exp = e

Homework Equations


No clue how to start this

The Attempt at a Solution


Y'=A=dY/dt
Y=At+C3 (not sure)

A'-(A^2)+C1exp(At+C3)-C2=0
A'-(A^2)+C1exp(C3)exp(At)=0
let C=C1*exp(C3)
A'-(A^2)+Cexp(At)=0
Please post your HW threads in the proper HW forum by subject. If you're not sure where they should go, you can always ask a Mentor for help.
 
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1. What is a 2nd order Ordinary Differential Equation?

A 2nd order Ordinary Differential Equation (ODE) is an equation that relates a function to its derivatives. It includes the first and second derivatives of the function, but not higher order derivatives. It is often used to model real-world systems in physics, engineering, and other fields.

2. How do you solve a 2nd order Ordinary Differential Equation?

To solve a 2nd order ODE, you first need to identify the type of equation by looking at its form. The three main types are linear, separable, and exact. Then, you can use different methods such as substitution, integration, or power series to solve the equation. It is important to check the solution by plugging it back into the original equation.

3. Why are 2nd order Ordinary Differential Equations important?

2nd order ODEs are important because they can accurately describe and predict the behavior of many natural and man-made systems. They are used in a wide range of scientific fields, including physics, chemistry, biology, and economics. By solving these equations, scientists can understand and improve various processes and phenomena.

4. What are some applications of 2nd order Ordinary Differential Equations?

2nd order ODEs have numerous applications in science and engineering. Some examples include modeling the motion of a pendulum, analyzing the behavior of electrical circuits, predicting population growth in biology, and understanding the dynamics of chemical reactions. They also play a crucial role in the development of new technologies, such as control systems and image processing algorithms.

5. What are the challenges in solving 2nd order Ordinary Differential Equations?

Solving 2nd order ODEs can be challenging because there is no one universal method that can solve all types of equations. Each equation requires a different approach, and it may take several steps and techniques to arrive at a solution. Additionally, some equations may not have analytical solutions, and numerical methods must be used instead. It is also essential to pay attention to initial or boundary conditions, as they can significantly affect the solution of the equation.

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